1. @ Brookhaven National Laboratory April 2008 QCD Critical Point and Its Effects on Physical Observables Schematic Consideration Masayuki ASAKAWA Department of Physics, Osaka University in collaboration with C. Nonaka, B. Müller, S.A. Bass

2. M. Asakawa (Osaka University) QCD Phase Diagram CSC (color superconductivity) QGP (quark-gluon plasma) Hadron Phase T BB chiral symmetry breaking confinement order ? 1st order crossover CEP(critical end point) 160-190 MeV 5-10  0 100MeV ~ 10 12 K RHIC LHC

3. M. Asakawa (Osaka University) 20th Anniversary of CEP in QCD

4. M. Asakawa (Osaka University) Where is CEP, if any? Stephanov,hep-lat/0701002

5. M. Asakawa (Osaka University) CEP = 2nd order phase transition, but... If expansion is adiabatic Divergence of Fluctuation Correlation Length Specific Heat ? CEP = 2nd Order Phase Transition Point 2SC CFL even if the system goes right through the critical end point… There is no conservation law that slows down the change of those quantities ! Subject to Final State Interactions

6. M. Asakawa (Osaka University) Furthermore... Furthermore, critical slowing down limits the size of fluctuation, correlation length ! fluctuation ~   Time Evolution along given isentropic trajectories (n B /s : fixed) Model H (Hohenberg and Halperin RMP49(77)435)  and  eq little difference

7. M. Asakawa (Osaka University) Principles to Look for Other Observables We are in need of observables that are not subject to final state interactions After Freezeout, no effect of final state interactions Chemical Freezeout usually assumed momentum independent but this is not right chemical freezeout time: p T (or y T ) dependent Larger p T (or y T ), earlier ch. freezeout Principle I

8. M. Asakawa (Osaka University) Emission Time Distribution Emission Time Larger y T, earlier emission To minimize resonance effect, y T is used instead of p T No CEP effect (UrQMD)

9. M. Asakawa (Osaka University) Principle II Universality : QCD CEP belongs to the same universality class as 3d Ising Model Universality : QCD CEP belongs to the same universality class as 3d Ising Model Lattice QCD at finite density: still in its infancy For critical behavior: need to carry out V limit ( T,   ) ( r,h ) QCD Critical End Point 3d Ising Model End Point same universality class h : external magnetic field

10. M. Asakawa (Osaka University) What is not universal Further Assumptions Mapping T r h is not an assumption Size of Critical Region No general universality Lattice calculation: not yet V  limit Renormalization group analysis in Effective Models ? need to be treated as an input, at the moment

11. M. Asakawa (Osaka University) EOS on Ising Side Critical Behavior on Ising Side h : external magnetic field parametric representation R. Guida and J. Zinn-Justin, NPB486 (1997) 626 1st order cross over CEP Condition for M 0 and h 0

12. M. Asakawa (Osaka University) Singular Part + Non-singular Part Matched Entropy Density Hadron Phase (excluded volume model) QGP phase Dimensionless Quantity: S c D: related to extent of critical region Matching between Hadronic and QGP EOS Entropy Density consists of Singular and Non-Singular Parts Requirement: reproduce both the singular behavior and know asymptotic limits Only Singular Part shows universal behavior crit  Bcrit

13. M. Asakawa (Osaka University) Isentropic Trajectories In each volume element, Entropy (S) and Baryon Number (N B ) are conserved, as long as entropy production can be ignored (= when viscosities are small) Isentropic Trajectories (n B /s = const.) Near CEP s and n B changes rapidly isentropic trajectories show non-trivial behavior Bag Model EOS case An Example CEP

14. M. Asakawa (Osaka University) With Large Critical Region without CEP (EOS in usual hydro calculation) with CEP Focusing of Isentropic Trajectories Excluded Volume Approximation + Bag Model EOS No Focusing used in most hydro calculations

15. M. Asakawa (Osaka University) Consequence ratio For a given chemical freezeout point, prepare two isentropic trajectories: w/ and w/o CEP Bag QCE Along isentropic trajectory: As a function of p T (y T ): Bag QCE Principle I : near CEP steeper

16. M. Asakawa (Osaka University) Evolution along Isentropic Trajectory with QCE steeper spectra at high P T

17. M. Asakawa (Osaka University) Effect on Spectra ? NA49, PRC73, 044910(2006) steeper spectra at high P T

18. M. Asakawa (Osaka University) Result of One Temperature Fit Only one experimental result for slope Still error bar is large NA49, PRC73, 044910(2006)

19. M. Asakawa (Osaka University) Summary Two Principles: i) Chemical Freezeout is p T (y T ) dependent ii) Isentropic Trajectory behaves non-trivially near CEP (focusing) ratio behaves non-monotonously near CEP We then made a data search Information on the QCD critical point: such as location, size of critical region,existence… turned out NA49 data shows non-trivial behavior around 40 GeV/A still error bar is large, finer energy scans at SPS, FAIR, RHIC: desirable Effect on Flow ? c s changes differently from the case with EOS used in usual hydro cal. (3D hydro cal. with CEP + UrQMD: C. Nonaka in progress)